At Least Four Distinct Circadian Regulatory Mechanisms Are Required for All Phases of Rhythms in mRNA Amount

Since the advent of techniques to investigate gene expression on a large scale, numerous circadian rhythms in mRNA amount have been reported. These rhythms generally differ in amplitude and phase. The authors investigated how far a parameter not regulated by the circadian clock can influence the phase of a rhythm in RNA amount arising from a circadian rhythm of transcription. Using a discrete-time approach, they modeled a sinusoidal rhythm in transcription with various constant exponential RNA decay rates. They found that the slower the RNA degradation, the later the phase of the RNA amount rhythm compared with the phase of the transcriptional rhythm. However, they also found that the phase of the RNA amount rhythm is limited to a timeframe spanning the first quarter of the period following the phase of the transcriptional rhythm. This finding is independent of the amplitude and vertical shift of the transcriptional rhythm or even of the way constant RNA degradation is modeled. The authors confirmed their results with a continuous-time model, which allowed them to derive a simple formula relating the phase of the RNA amount rhythm solely to the phase and period of its sinusoidal transcriptional rhythm and its constant RNA half-life. This simple formula even holds true for the best sinusoidal approximations of a nonsinusoidal rhythm of transcription and RNA amount. When expanding the model to include additional events with constant exponential kinetics, such as RNA processing, they found that each event expands the phase limit by another quarter of the period when it occurs in sequence but not when it occurs as a competing process. However, the limit expansion comes at the price of minuscule amplitudes. When using a discrete-time approach to model constant rates of transcription with a sinusoidal RNA half-life, the authors found that the phase of the RNA amount rhythm is unaffected by changes in the constant rate of transcription. In summary, their data show that at least 4 distinct circadian regulatory mechanisms are required to allow for all phases in rhythms of RNA amount, one for each quarter of the period.